It depends on server economy but inscription can generally be leveled at a profit, provided you check the AH to make sure you're not crafting useless glyphs while leveling and you're willing to take time to sell them after they're crafted. you won't make the profit while actually leveling but as long as you keep and eventually sell what you make you'll most likely end up better off. Enchanting can turn a profit to level as well sometimes, it depends on the demand for older enchants on your server.

Beyond that from most expensive to least expensive to level I'd say Leatherworking > Blacksmithing > Tailoring > Engineering > Jewelcrafting > Enchancting > Alchemy > Inscription. Depends a bit of server but it'll be around about that with minor variations on most.

Cheapest from the list would be scribe...the first time I leveled it, a few years ago now, I made all my money back selling glyphs. Cost me maybe 4k the second time, farming a total of zero herbs both times. Also takes about an hour and a half to level all the way to 600, assuming there is enough stuff on the AH. If all you are looking for is a cheap and easy profession to level to max in one sitting without having to farm for jack shit, look no further.

Inscription was very easy to level, although I did it back in Cata from 1-525. I may have spent 1-2k total on miscellaneous low level herbs. Cost less than that to go from 525-600.

Tailoring would be good, also, but I remember going through frostweave (even during Wrath) and it was brutal. IIRC, you'll need around 1200 frostweave in order to get to embersilk. Would check wow-professions but unable to currently.

I haven't had an engi below 450 since wrath but on my server engi and JC have always been the most expensive. But a lot of low level mining ores have gone down in price. I leveled BS on my rogue buying ores and smelting on m miner (yes I'm that lazy) and did BS for less than 7k. So I do suppose engi and JC would be cheaper than blacksmithing probably.

If you meant easy when you said cheap then Profession that requires a farming skill is always free. It will just consume your time and not one penny in your bank ever used. Looking at all the profession, there all free. They just takes time and effort farming.

...but if you meant low prize when you said cheap and want max level just with auction house, which you forgot to specify.
No one can give you the right answer since like what you said its all server dependent. The problem here is you havent told us what server and fraction you are in. Tell us, then you might get lucky and someone from it might do the research for you and tell you about it.

If you meant easy when you said cheap then Profession that requires a farming skill is always free. It will just consume your time and not one penny in your bank ever used. Looking at all the profession, there all free. They just takes time and effort farming.

...but if you meant low prize when you said cheap and want max level just with auction house, which you forgot to specify.
No one can give you the right answer since like what you said its all server dependent. The problem here is you havent told us what server and fraction you are in. Tell us, then you might get lucky and someone from it might do the research for you and tell you about it.

Due to the nature of how people acquire the mats that go into any profession, relatively the list shouldn't change. Inscription should be cheaper just due to more random herbs on the AH than say skins for LW. Now inscription may cost more on his server than mine by it should still probably be cheaper than LW or whatever due to its nature.